Finite Group Databasebeta

← #26221298

Subgroups — #26221298

Order 12032.

1184 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689653C211yesmaximal, characteristic
2C2×#15689181C211yesmaximal, characteristic, complemented
3C2×#15689081C211yesmaximal, characteristic, complemented
4#20244326C211yesmaximal, characteristic, complemented
5#20244322C211yesmaximal, characteristic, complemented
6#20244184C211yesmaximal, characteristic, complemented
7#20244180C211yesmaximal, characteristic, complemented
8#20243685C211yesmaximal, characteristic, complemented
9#20243681C211yesmaximal, characteristic, complemented
10#20243678C211yesmaximal, characteristic, complemented
11#20243153C211yesmaximal, characteristic, complemented
12#20243153C211yesmaximal, characteristic, complemented
13#20243152C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic47C211yesmaximal, characteristic, complemented
15C47×#1870C211yesmaximal, characteristic, complemented
16C23×C47⋊C8C2211yescharacteristic
17#15689653—24no—
18#15689653—24no—
19C2×#13094019C411yescharacteristic
20C2×#13094017C411yescharacteristic
21C2×#13094014C411yescharacteristic
22C2×#13094010C411yescharacteristic
23C2×#13094008C411yescharacteristic
24C2×#13094005C411yescharacteristic
25C2×#13094001C411yescharacteristic
26C2×#13093996C411yescharacteristic
27C2×C4×Dic94C2211yescharacteristic
28C2×C4×C22⋊D47C2211yescharacteristic
29C2×C4×C22⋊D47C2211yescharacteristic
30C2×#13093983C2211yescharacteristic
31C2×#13093981C2211yescharacteristic
32C22×C4×Dic47C2211yescharacteristic
33#15689181—24no—
34C2×Dic47⋊C8C2211yescharacteristic
35C2×Dic47⋊C8C2211yescharacteristic
36C2×C22⋊(C47⋊C8)C2211yescharacteristic
37C2×C22⋊(C47⋊C8)C2211yescharacteristic
38C2×C22⋊(C47⋊C8)C2211yescharacteristic
39C2×(C2×D47)⋊C8C2211yescharacteristic
40C2×(C2×D47)⋊C8C2211yescharacteristic
41C2×(C2×D47)⋊C8C2211yescharacteristic
42C2×(C2×D47)⋊C8C2211yescharacteristic
43#15689081—24no—
44C2×#13093934C2211yescharacteristic
45C2×#13093934C2211yescharacteristic
46C2×#13093934C2211yescharacteristic
47C2×C8×Dic47C2211yescharacteristic
48C2×C8×Dic47C2211yescharacteristic
49C2×C8×Dic47C2211yescharacteristic
50#15688878C2211yescharacteristic
51#15688878C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54#15688877C2211yescharacteristic
55#15688877C2211yescharacteristic
56C22×M16×C47C2211yescharacteristic
57C2×C4×D4×C47C2211yescharacteristic
58C2×C22⋊C8×C47C2211yescharacteristic
59C2×C22⋊C8×C47C2211yescharacteristic
60C2×C22⋊C8×C47C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C22×Dic94C2×C411yescharacteristic
64C22×C22⋊D47C2×C411yescharacteristic
65C22×C22⋊D47C2×C411yescharacteristic
66C23×Dic47C2×C411yescharacteristic
67C23×Dic47C2×C411yescharacteristic
68C22×C4×D47C2311yescharacteristic
69C22×C47⋊C8—22no—
70C22×C47⋊C8—22no—
71C22×C47⋊C8—22no—
72C22×C47⋊C8C2311yescharacteristic
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75C22×C47⋊C8C2311yescharacteristic
76#13094019—24no—
77#13094017—24no—
78#13094014—24no—
79#13094010—24no—
80#13094008—24no—
81#13094005—24no—
82#13094001—24no—
83#13093996—24no—
84C4×Dic94—22no—
85C4×Dic94—22no—
86C4×C22⋊D47—22no—
87C4×C22⋊D47—22no—
88C4×C22⋊D47—22no—
89C4×C22⋊D47—22no—
90#13093983D414yes—
91#13093983D414yes—
92#13093981—22no—
93#13093981—22no—
94C2×C4⋊Dic47C2×C411yescharacteristic
95C2×C4⋊Dic47C2×C411yescharacteristic
96C2×C4⋊Dic47C2×C411yescharacteristic
97C2×Dic47⋊C4C2×C411yescharacteristic
98C2×Dic47⋊C4C2×C411yescharacteristic
99C2×Dic47⋊C4C2×C411yescharacteristic
100C2×Dic47⋊C4C2×C411yescharacteristic
101C2×Dic47⋊C4C2×C411yescharacteristic
102C2×Dic47⋊C4C2×C411yescharacteristic
103C2×C22⋊Dic47C2×C411yescharacteristic
104C2×C22⋊Dic47C2×C411yescharacteristic
105C2×C22⋊Dic47C2×C411yescharacteristic
106C2×C22⋊Dic47C2×C411yescharacteristic
107C2×(C2×D47)⋊C4C2×C411yescharacteristic
108C2×(C2×D47)⋊C4C2×C411yescharacteristic
109C2×(C2×D47)⋊C4C2×C411yescharacteristic
110C2×(C2×D47)⋊C4C2×C411yescharacteristic
111C2×C4×Dic47—22no—
112C2×C4×Dic47—22no—
113C2×C4×Dic47C2×C411yescharacteristic
114C2×C4×Dic47C2×C411yescharacteristic
115C2×C4×Dic47C2311yescharacteristic
116C2×C4×Dic47C2311yescharacteristic
117C2×C4×Dic47C2311yescharacteristic
118Dic47⋊C8—22no—
119Dic47⋊C8—22no—
120C22⋊(C47⋊C8)—22no—
121C22⋊(C47⋊C8)—22no—
122C22⋊(C47⋊C8)—22no—
123(C2×D47)⋊C8—22no—
124(C2×D47)⋊C8—22no—
125(C2×D47)⋊C8—22no—
126(C2×D47)⋊C8—22no—
127#13093934—22no—
128#13093934—22no—
129#13093934—22no—
130C8×Dic47—22no—
131C8×Dic47—22no—
132C8×Dic47—22no—
133C22×D4×C47C2×C411yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C23×C4×C47C2311yescharacteristic
136C2×M16×C47—22no—
137C2×M16×C47—22no—
138C2×M16×C47—22no—
139C22×C8×C47C2311yescharacteristic
140C22×C8×C47C2311yescharacteristic
141C22×C8×C47C2311yescharacteristic
142C22×C8×C47C2311yescharacteristic
143C4×D4×C47—22no—
144C4×D4×C47—22no—
145C2×C4⋊C4×C47C2×C411yescharacteristic
146C2×C22⋊C4×C47C2×C411yescharacteristic
147C2×C22⋊C4×C47C2×C411yescharacteristic
148C2×C42×C47C2311yescharacteristic
149C22⋊C8×C47—22no—
150C22⋊C8×C47—22no—
151C22⋊C8×C47—22no—
152C24×C47C22×C411yescharacteristic
153C24×C47C22×C411yescharacteristic
154C23×D47C22×C411yescharacteristic
155C2×D4×C47—22no—
156C2×D4×C47—22no—
157C2×D4×C47—41no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47C22×C411yescharacteristic
169C22×C4×C47C22×C411yescharacteristic
170C22×C4×C47C22×C411yescharacteristic
171C22×C4×C47C22×C411yescharacteristic
172C22×C4×C47C2×D412yes—
173C22×C4×C47C2×D412yes—
174C22×C4×C47C2411yescharacteristic
175C2×C22⋊D47—22no—
176C2×C22⋊D47—22no—
177C2×C22⋊D47—22no—
178C2×C22⋊D47—22no—
179C2×C22⋊D47—41no—
180C2×C22⋊D47—41no—
181C22×Dic47—22no—
182C22×Dic47—22no—
183C22×Dic47—22no—
184C22×Dic47—22no—
185C22×Dic47—41no—
186C22×Dic47—41no—
187C22×Dic47C22×C411yescharacteristic
188C22×Dic47C22×C411yescharacteristic
189C22×Dic47C22×C411yescharacteristic
190C22×Dic47C22×C411yescharacteristic
191C22×Dic47C22×C411yescharacteristic
192C22×Dic47C22×C411yescharacteristic
193C22×Dic47C22×C411yescharacteristic
194C2×C4×D47—21no—
195C2×C4×D47—21no—
196C2×C4×D47—21no—
197C2×C4×D47—21no—
198C2×C4×D47—21no—
199C2×C4×D47—21no—
200C2×Dic94—22no—
201C2×Dic94—22no—
202C2×Dic94—41no—
203M16×C47—28no—
204C2×C8×C47—21no—
205C2×C8×C47—21no—
206C2×C8×C47—21no—
207C2×C8×C47—21no—
208C2×C8×C47—21no—
209C2×C8×C47—21no—
210C2×C8×C47—21no—
211C2×C8×C47—21no—
212C2×C8×C47—21no—
213C2×C8×C47—21no—
214C2×C8×C47#4112yes—
215C2×C8×C47#4112yes—
216C4⋊C4×C47—22no—
217C22⋊C4×C47—22no—
218C22⋊C4×C47—22no—
219C42×C47—21no—
220C42×C47—21no—
221C22⋊Dic47—22no—
222C22⋊Dic47—22no—
223C22⋊Dic47C22⋊C414yes—
224C22⋊Dic47C22⋊C414yes—
225(C2×D47)⋊C4—22no—
226(C2×D47)⋊C4—22no—
227(C2×D47)⋊C4—22no—
228(C2×D47)⋊C4—22no—
229C4⋊Dic47—22no—
230C4⋊Dic47C22⋊C414yes—
231C4⋊Dic47C22⋊C414yes—
232Dic47⋊C4—22no—
233Dic47⋊C4—22no—
234Dic47⋊C4—22no—
235Dic47⋊C4—22no—
236Dic47⋊C4—22no—
237Dic47⋊C4—22no—
238C4×Dic47—21no—
239C4×Dic47—21no—
240C4×Dic47—22no—
241C4×Dic47—22no—
242C4×Dic47C2×D412yes—
243C4×Dic47C2×D412yes—
244C4×Dic47C2×D412yes—
245C4×Dic47C2×D412yes—
246C2×C47⋊C8—28no—
247C2×C47⋊C8—21no—
248C2×C47⋊C8—21no—
249C2×C47⋊C8—21no—
250C2×C47⋊C8—21no—
251C2×C47⋊C8—21no—
252C2×C47⋊C8—21no—
253C2×C47⋊C8—21no—
254C2×C47⋊C8—21no—
255C2×C47⋊C8—21no—
256C2×C47⋊C8—21no—
257C2×C47⋊C8#4112yes—
258C2×C47⋊C8#4112yes—
259C23×C47—21no—
260C23×C47—21no—
261C23×C47—21no—
262C23×C47—21no—
263C23×C47—21no—
264C23×C47—21no—
265C23×C47—21no—
266C23×C47—21no—
267C23×C47—21no—
268C23×C47—21no—
269C23×C47—21no—
270C23×C47—21no—
271C23×C47C2×C22⋊C412yes—
272C23×C47#13112yes—
273C23×C47C23×C411yescharacteristic
274C22×D47—21no—
275C22×D47—21no—
276C22×D47—21no—
277C22×D47—21no—
278C22×D47—21no—
279C22×D47—21no—
280C22×D47—21no—
281D4×C47—44no—
282C2×C4×C47—21no—
283C2×C4×C47—21no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—21no—
289C2×C4×C47—21no—
290C2×C4×C47—21no—
291C2×C4×C47—21no—
292C2×C4×C47—21no—
293C2×C4×C47—21no—
294C2×C4×C47—21no—
295C2×C4×C47—21no—
296C2×C4×C47—21no—
297C2×C4×C47—41no—
298C2×C4×C47—41no—
299C2×C4×C47—41no—
300C2×C4×C47—41no—
301C2×C4×C47C2×C22⋊C412yes—
302C2×C4×C47C22×D411yescharacteristic
303C2×C4×C47C22×D411yescharacteristic
304C2×C4×C47C2×#4111yescharacteristic
305C2×C4×C47C2×#4111yescharacteristic
306C2×C4×C47C2×#4111yescharacteristic
307C2×C4×C47C2×#4111yescharacteristic
308C22⋊D47—44no—
309C22⋊D47—44no—
310C2×Dic47—21no—
311C2×Dic47—21no—
312C2×Dic47—21no—
313C2×Dic47—21no—
314C2×Dic47—21no—
315C2×Dic47—21no—
316C2×Dic47—21no—
317C2×Dic47—21no—
318C2×Dic47—21no—
319C2×Dic47—21no—
320C2×Dic47—21no—
321C2×Dic47—21no—
322C2×Dic47—21no—
323C2×Dic47—21no—
324C2×Dic47—21no—
325C2×Dic47—21no—
326C2×Dic47—44no—
327C2×Dic47—44no—
328C2×Dic47C2×C22⋊C412yes—
329C2×Dic47C2×C22⋊C412yes—
330C2×Dic47C2×C22⋊C412yes—
331C2×Dic47C2×C22⋊C412yes—
332C2×Dic47#13112yes—
333C4×D47—41no—
334C4×D47—41no—
335C4×D47—41no—
336C4×D47—41no—
337Dic94—44no—
338C8×C47—22no—
339C8×C47—22no—
340C8×C47—41no—
341C8×C47—41no—
342C47⋊C8—22no—
343C47⋊C8—22no—
344C47⋊C8—41no—
345C47⋊C8—41no—
346#21381—471nomaximal, Sylow
347C22×C47—22no—
348C22×C47—22no—
349C22×C47—22no—
350C22×C47—22no—
351C22×C47—22no—
352C22×C47—22no—
353C22×C47—41no—
354C22×C47—41no—
355C22×C47—41no—
356C22×C47—41no—
357C22×C47—41no—
358C22×C47—41no—
359C22×C47—41no—
360C22×C47—41no—
361C22×C47C22×C22⋊C411yescharacteristic
362C22×C47C4×#4111yescharacteristic
363C22×C47C4×#4111yescharacteristic
364C22×C47C2×#13111yescharacteristic
365C22×C47C2×#13111yescharacteristic
366C22×C47#56811yescharacteristic
367C22×C47#56811yescharacteristic
368C2×D47—41no—
369C2×D47—41no—
370C2×D47—41no—
371C2×D47—41no—
372C2×D47—41no—
373C2×D47—41no—
374C2×D47—41no—
375C4×C47—22no—
376C4×C47—41no—
377C4×C47—41no—
378C4×C47—41no—
379C4×C47#52511yescharacteristic
380C4×C47#52511yescharacteristic
381C4×C47#53211yescharacteristic
382C4×C47#53211yescharacteristic
383Dic47—22no—
384Dic47—22no—
385Dic47—22no—
386Dic47—22no—
387Dic47—22no—
388Dic47—41no—
389Dic47—41no—
390C2×#529—471no—
391C2×#433—471no—
392C2×#405—471no—
393#1985—471no—
394#1984—471no—
395#1955—471no—
396#1954—471no—
397#1870—471no—
398#1870D4711yescharacteristic, complemented
399#1869—471no—
400#1869—471no—
401#1750—471no—
402#1750—471no—
403#1749—471no—
404C4×C22⋊C8—471no—
405C2×C47—42no—
406C2×C47—42no—
407C2×C47#229711yescharacteristic
408C2×C47#288011yescharacteristic
409C2×C47#288011yescharacteristic
410C2×C47#296611yescharacteristic
411C2×C47#296711yescharacteristic
412C2×C47#296811yescharacteristic
413C2×C47#296911yescharacteristic
414D47—81no—
415C22×M16C2×D4711yescharacteristic
416C23×C8—471no—
417#529—944no—
418#529—944no—
419C2×#126—471no—
420C2×#126—471no—
421C2×#125—471no—
422C2×#124—471no—
423C2×#123—471no—
424C2×#123—471no—
425C2×C22⋊Q8—471no—
426C2×#121—471no—
427C2×C4×Q8—471no—
428C2×C4×D4—471no—
429C2×C4×D4—471no—
430C2×C4×D4C2×D4711yescharacteristic
431C2×#117—471no—
432C2×#117—471no—
433C22×C42—471no—
434#433—944no—
435C2×C4⋊C8—471no—
436C2×C4⋊C8—471no—
437C2×C22⋊C8—471no—
438C2×C22⋊C8—471no—
439C2×C22⋊C8—471no—
440C2×C22⋊C8—471no—
441C2×C22⋊C8—471no—
442C2×C22⋊C8—471no—
443C2×C22⋊C8—471no—
444C2×C22⋊C8C2×D4711yescharacteristic
445C2×C22⋊C8C2×D4711yescharacteristic
446C2×C22⋊C8C2×D4711yescharacteristic
447#405—944no—
448C2×#97—471no—
449C2×#97—471no—
450C2×#97—471no—
451C2×C4×C8—471no—
452C2×C4×C8—471no—
453C2×C4×C8—471no—
454#336—471no—
455#336—471no—
456#336—471no—
457#336—471no—
458#336—471no—
459#336—471no—
460#336C2×D4711yescharacteristic
461#336C2×D4711yescharacteristic
462C47#2138111yescharacteristic, complemented, Sylow
463C22×Q8—471no—
464C22×D4—471no—
465C22×D4—471no—
466C22×D4C4×D4711yescharacteristic
467C23×C4—471no—
468C23×C4—471no—
469C23×C4—471no—
470C23×C4C22×D4711yescharacteristic
471C23×C4C22×D4711yescharacteristic
472C2×M16—22no—
473C2×M16—22no—
474C2×M16—22no—
475C22×C8—471no—
476C22×C8—471no—
477C22×C8—471no—
478C22×C8—471no—
479C22×C8—942no—
480C22×C8—942no—
481C22×C8—942no—
482C22×C8C22×D4711yescharacteristic
483C22×C8C22×D4711yescharacteristic
484C22×C8C22×D4711yescharacteristic
485C22×C8C22×D4711yescharacteristic
486#126—944no—
487#126—944no—
488#125—944no—
489#124—944no—
490#123—944no—
491#123—944no—
492C22⋊Q8—944no—
493#121—944no—
494C4×Q8—942no—
495C4×Q8—942no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—942no—
499C4×D4—942no—
500C4×D4—942no—
501C4×D4—942no—
502#117—474no—
503#117—474no—
504#117—942no—
505#117—942no—
506C2×C4⋊C4—471no—
507C2×C4⋊C4—471no—
508C2×C4⋊C4—471no—
509C2×C4⋊C4—471no—
510C2×C4⋊C4—471no—
511C2×C4⋊C4—471no—
512C2×C4⋊C4—471no—
513C2×C4⋊C4—471no—
514C2×C4⋊C4—471no—
515C2×C4⋊C4C4×D4711yescharacteristic
516C2×C22⋊C4—471no—
517C2×C22⋊C4—471no—
518C2×C22⋊C4—471no—
519C2×C22⋊C4—471no—
520C2×C22⋊C4—471no—
521C2×C22⋊C4—471no—
522C2×C22⋊C4—471no—
523C2×C22⋊C4—471no—
524C2×C22⋊C4C4×D4711yescharacteristic
525C2×C22⋊C4C4×D4711yescharacteristic
526C2×C42—471no—
527C2×C42—471no—
528C2×C42—471no—
529C2×C42—471no—
530C2×C42—471no—
531C2×C42—942no—
532C2×C42—942no—
533C2×C42C22×D4711yescharacteristic
534C4⋊C8—942no—
535C4⋊C8—942no—
536C22⋊C8—22no—
537C22⋊C8—22no—
538C22⋊C8—22no—
539C22⋊C8—942no—
540C22⋊C8—942no—
541C22⋊C8—942no—
542C22⋊C8—942no—
543C22⋊C8—942no—
544C22⋊C8—942no—
545C22⋊C8—942no—
546#97—942no—
547#97—942no—
548#97—942no—
549C4×C8—942no—
550C4×C8—942no—
551C4×C8—942no—
552C24—471no—
553C24C2×C4×D4711yescharacteristic
554C24C2×C4×D4711yescharacteristic
555C2×Q8—942no—
556C2×Q8—942no—
557C2×Q8—1881no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—41no—
561C2×D4—942no—
562C2×D4—942no—
563C2×D4—942no—
564C2×D4—942no—
565C2×D4—1881no—
566C2×D4—1881no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—471no—
578C22×C4—471no—
579C22×C4—471no—
580C22×C4—471no—
581C22×C4—471no—
582C22×C4—471no—
583C22×C4—471no—
584C22×C4—942no—
585C22×C4—942no—
586C22×C4—942no—
587C22×C4—942no—
588C22×C4—941no—
589C22×C4—941no—
590C22×C4—941no—
591C22×C4—941no—
592C22×C4—941no—
593C22×C4—941no—
594C22×C4—1881no—
595C22×C4—1881no—
596C22×C4C2×C4×D4711yescharacteristic
597C22×C4C2×C4×D4711yescharacteristic
598C22×C4C2×C4×D4711yescharacteristic
599C22×C4C2×C4×D4711yescharacteristic
600C22×C4D4×D4712yes—
601C22×C4D4×D4712yes—
602C22×C4C23×D4711yescharacteristic
603M16—28no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—472no—
615C2×C8—472no—
616C2×C8—948no—
617C2×C8—941no—
618C2×C8—941no—
619C2×C8—941no—
620C2×C8—941no—
621C2×C8—941no—
622C2×C8—941no—
623C2×C8—941no—
624C2×C8—941no—
625C2×C8—941no—
626C2×C8—941no—
627C2×C8#1062535212yes—
628C2×C8#1062535212yes—
629C4⋊C4—22no—
630C4⋊C4—474no—
631C4⋊C4—474no—
632C4⋊C4—942no—
633C4⋊C4—942no—
634C4⋊C4—942no—
635C4⋊C4—942no—
636C4⋊C4—942no—
637C4⋊C4—942no—
638C4⋊C4—942no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—474no—
642C22⋊C4—474no—
643C22⋊C4—942no—
644C22⋊C4—942no—
645C22⋊C4—942no—
646C22⋊C4—942no—
647C22⋊C4—942no—
648C22⋊C4—942no—
649C42—21no—
650C42—21no—
651C42—472no—
652C42—472no—
653C42—472no—
654C42—472no—
655C42—942no—
656C42—942no—
657C42—941no—
658C42—941no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—941no—
672C23—941no—
673C23—941no—
674C23—941no—
675C23—941no—
676C23—941no—
677C23—941no—
678C23C22⋊C4×D4712yes—
679C23#1309403212yes—
680C23C22×C4×D4711yescharacteristic
681Q8—1884no—
682D4—44no—
683D4—1884no—
684D4—1884no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—472no—
705C2×C4—472no—
706C2×C4—472no—
707C2×C4—472no—
708C2×C4—472no—
709C2×C4—941no—
710C2×C4—941no—
711C2×C4—941no—
712C2×C4—941no—
713C2×C4—941no—
714C2×C4—941no—
715C2×C4—941no—
716C2×C4—941no—
717C2×C4—941no—
718C2×C4—941no—
719C2×C4—941no—
720C2×C4—941no—
721C2×C4—941no—
722C2×C4—941no—
723C2×C4—941no—
724C2×C4—941no—
725C2×C4—1884no—
726C2×C4—1884no—
727C2×C4—1881no—
728C2×C4—1881no—
729C2×C4—1881no—
730C2×C4—1881no—
731C2×C4C22⋊C4×D4712yes—
732C2×C4C2×D4×D4711yescharacteristic
733C2×C4C2×D4×D4711yescharacteristic
734C2×C4#41×D4711yescharacteristic
735C2×C4#41×D4711yescharacteristic
736C2×C4C2×#1062535211yescharacteristic
737C2×C4C2×#1062535211yescharacteristic
738C8—22no—
739C8—22no—
740C8—41no—
741C8—41no—
742C8—942no—
743C8—942no—
744C8—1881no—
745C8—1881no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—1881no—
761C22—1881no—
762C22—1881no—
763C22—1881no—
764C22—1881no—
765C22—1881no—
766C22—1881no—
767C22C2×C22⋊C4×D4711yescharacteristic
768C22C4×#1062535211yescharacteristic
769C22C4×#1062535211yescharacteristic
770C22#131×D4711yescharacteristic
771C22C2×#1309403211yescharacteristic
772C22#1568988811yescharacteristic
773C22#1568988911yescharacteristic
774C4—22no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—942no—
779C4—942no—
780C4—942no—
781C4—942no—
782C4—942no—
783C4—1881no—
784C4—1881no—
785C4#1568962911yescharacteristic
786C4#1568963111yescharacteristic
787C4#1568966811yescharacteristic
788C4#1568966811yescharacteristic
789C2—42no—
790C2—42no—
791C2—3761no—
792C2#2024587311yescharacteristic
793C2#2025183611yescharacteristic
794C2#2025183811yescharacteristic
795C2#2025235811yescharacteristic
796C2#2025237411yescharacteristic
797C2#2025238311yescharacteristic
798C2#2025238711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1870C2
prime radicalC2×#13093996C4
cosocleC22×C4×C47C24
hypercenter#1870D47
hypocenterC47#21381
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1870

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#15689181C2semidirect
3. C2×#15689081C2semidirect
4. #20244326C2semidirect
5. #20244322C2semidirect
6. #20244184C2semidirect
7. #20244180C2semidirect
8. #20243685C2semidirect
9. #20243681C2semidirect
10. #20243678C2semidirect
11. #20243153C2semidirect
12. #20243153C2semidirect
13. #20243152C2semidirect
14. C22⋊C8×Dic47C2semidirect
15. C47×#1870C2semidirect
398. #1870D47semidirect
462. C47#21381semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#156896532
C2×#156891812
C2×#156890812
#202443262
#202443222
#202441842
#202441802
#202436852
#202436812
#202436782
#202431532
#202431522
C22⋊C8×Dic472
C47×#18702
#2138147